Logarithms And Logarithmic Functions Worksheet With Answers Page 19
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27ANSWER:
a. 264 h or 11 days
b. 49.5 h or about 2 days 1.5 h
b . ≈ 3 years
7-3 Logarithms and Logarithmic Functions
c .
h or 20 min
c. ≈ 4.5 years
60. WRITING IN MATH What should you consider
59. FINANCIAL LITERACY Jacy has spent $2000
when using exponential and logarithmic models to
on a credit card. The credit card company charges
make decisions?
24% interest, compounded monthly. The credit card
SOLUTION:
company uses
to determine
Sample answer: Exponential and logarithmic models
how much time it will be until Jacy’s debt reaches a
can grow without bound, which is usually not the
certain amount, if A is the amount of debt after a
case of the situation that is being modeled. For
period of time, and t is time in years.
instance, a population cannot grow without bound
due to space and food constraints. Therefore, when
a. Graph the function for Jacy’s debt.
using a model to make decisions, the situation that is
b. Approximately how long will it take Jacy’s debt to
being modeled should be carefully considered.
double?
c. Approximately how long will it be until Jacy’s debt
ANSWER:
triples?
Sample answer: Exponential and logarithmic models
can grow without bound, which is usually not the
SOLUTION:
case of the situation that is being modeled. For
a.
instance, a population cannot grow without bound
Graph of the function for Jacy’s debt:
due to space and food constraints. Therefore, when
using a model to make decisions, the situation that is
being modeled should be carefully considered.
61. CCSS ARGUMENTS Consider y = log
x in which
b
b, x, and y are real numbers. Zero can be in the
domain sometimes, always or never. Justify your
answer.
SOLUTION:
Never; if zero were in the domain, the equation
y
would be y = log
0. Then b
= 0. However, for any
b
b. It will take about 3 years for Jacy’s debt to
real number b, there is no real power that would let
double.
y
b
= 0
c. It will take about 4 years for Jacy’s debt to triple.
ANSWER:
ANSWER:
Never; if zero were in the domain, the equation
a.
y
would be y = log
0. Then b
= 0. However, for any
b
real number b, there is no real power that would let
y
b
= 0
62. ERROR ANALYSIS Betsy says that the graphs of
all logarithmic functions cross the y-axis at (0, 1)
because any number to the zero power equals 1.
Tyrone disagrees. Is either of them correct? Explain
your reasoning.
SOLUTION:
b . ≈ 3 years
Tyrone; sample answer: The graphs of logarithmic
c. ≈ 4.5 years
functions pass through (1, 0) not (0, 1).
60. WRITING IN MATH What should you consider
ANSWER:
when using exponential and logarithmic models to
eSolutions Manual - Powered by Cognero
Tyrone; sample answer: The graphs of logarithmic
Page 19
make decisions?
functions pass through (1, 0) not (0, 1).
SOLUTION:
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